No. Adrenaline is released by the sympathetic nervous system only in cases of stress.
If you put a heart in a liquid that contains water, electrolites and glucose you will see it will continue to beat constantly for quite some time...

"As a biologist, I firmly believe that when you're dead, you're dead. Except for what you live behind in history. That's the only afterlife" - J. Craig Venter

Yes, the initiation of the heartbeat is fired by the pacemaker (SA) which will rhythmically by AV. In normal condition, the impulse will be transmitted by neurotransmitter not a hormone.

The hormone, epinephrine/norepinephrine will be secreted in special condition like in physical or mentally stressness, which will act to excite the transmission of the impulse (excitator). That's why the heartbeat is increasing when we got stress.